How to get rid of the damn things..

They look like brambles to me. The one leaf looks too coarse for rose and the thorns are right for bramble.
I'd dig them out, being careful to dig out any runners, not just pull them. They love to run around and root all over the place

 

Them's definitely Brambles.

 

Can't I just set them on fire or something? Why does this all involve physical labour...

 

'fraid you'll just have to digem up n then burnem. Which indeed I find very satisfying, they usually crackle well
Other alternative is brush killing herbicide, but depending what you use may make the ground useless for anything else for a while. As there are virtually no leaves you won't be able to use a systemic. Yep, nothing for it - digem up n burnem

 

Once you get the early work done if you keep on top of things, it's not too bad. You'll have some hard work on your new allotment too. It will be worth it though.

 

They don't go that deep, I dug out a big well established patch next to a fence in about an hour or so.

 

Yes, I agree. It's the tips that root as runners that are a pain, because they can be small and you miss them and before you know it there's a new plant

 

Just like bindweed (got the tshirt) you have to be vigilant I guess.

 

Brambles 1 - fork 0

 

Managed to get as much as I could out, but it seems the source is behind the back fence in the neighbour's garden. Going to have to keep an eye on them and grab them as they spring up I think.

 

They look like they're in you chicken run,if so when you get your chooks scatter a bit of corn around them the chooks will do the rest great labourers they are